you want to expand the garden by planting a border of flowers. the border will have the same width around the entire garden.the flowers you brought will fill an area of 276sq.ft. How wide should the border be?

The inside is 24ft by 16ft but i need to find x.

Show your work by writing an equation to model the situation. This will set you on the right track...

(I made a mistake. The border is an addition, so this is the correct info...)

It will be very helpful to draw a diagram to model this situation.

Since you're given the dimensions of the garden, calculate the area of the garden without the border addition.

Add the given area of the flowers to get the area of the entire garden with the addition.

The width of the flower border is x. Now write an equation for the area of the entire garden with the border addition using x. (Refer to your diagram to help you.) What equation do you get?

To find the width of the border, let's first calculate the total area of the garden, including the inside and the border.

The inside area of the garden is given as 24 ft by 16 ft, so the inside area is:

Inside Area = Length × Width
Inside Area = 24 ft × 16 ft
Inside Area = 384 sq.ft.

Now, let's assume the width of the border is x ft, so the total dimensions of the enlarged garden would be (24 + 2x) ft by (16 + 2x) ft.

The total area of the enlarged garden would then be:

Total Area = (Length + 2x) × (Width + 2x)
Total Area = (24 ft + 2x) × (16 ft + 2x)
Total Area = 384 sq.ft. + 48x ft + 32x ft + 4x^2 sq.ft.

We are given that the flowers brought will fill an area of 276 sq.ft.

Therefore, the difference between the total area of the enlarged garden and the inside area should be equal to the area of the flowers. In other words:

Total Area - Inside Area = Flower Area
384 sq.ft. + 48x ft + 32x ft + 4x^2 sq.ft. - 384 sq.ft. = 276 sq.ft.

Simplifying the equation gives us:

80x + 4x^2 = 276 sq.ft.

Now, we can rearrange the equation and solve for x.

4x^2 + 80x - 276 = 0

To solve the quadratic equation, you can use factoring, completing the square, or the quadratic formula. In this case, let's use factoring.

(2x - 9)(2x + 31) = 0

Setting each factor equal to zero gives us:

2x - 9 = 0 or 2x + 31 = 0

Solving these equations gives us two possible values for x:

2x - 9 = 0
2x = 9
x = 9/2
x = 4.5 ft

or

2x + 31 = 0
2x = -31
x = -31/2
x = -15.5 ft

Since the width cannot be negative, we can disregard the negative value. Therefore, the width of the border should be 4.5 ft.

It will be very helpful to draw a diagram to model this situation.

Since you're given the dimensions of the garden, calculate the area of the entire garden.

Subtract the given area of the flowers to get the area of the "inside of the garden."

The width of the flower border is x. Now write an equation for the area of the inside of the garden using x. (Refer to your diagram to help you.) What equation do you get?

i found the answer x=3 but i don't kno how to show my work. lol